easy · Quantitative Finance

Under what structural condition does the linearity of expectation, defined as E[X + Y] = E[X] + E[Y], hold for two random variables X and Y?

1. It holds only if X and Y are normally distributed.
2. It holds for all random variables, regardless of their correlation or dependency.
3. It holds only if the covariance Cov(X, Y) = 0.
4. It holds only if X and Y are independent.

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